Empirical Exercise 4: Income Inequality
London School of Economics and Political Science
January 19, 2026
Today: Apply these tools to a real policy debate
The Spirit Level: Why Equality is Better for Everyone
If true, redistribution policies would:
One policy lever, multiple benefits
| Outcome | Coefficient | p-value | N |
|---|---|---|---|
| Trust | -6.54 | 0.000 | 23 |
| Mental Illness | +3.50 | 0.004 | 12 |
| Imprisonment | +0.29 | 0.001 | 23 |
| Child Conflict | +0.28 | 0.006 | 19 |
| Teenage Births | +5.86 | 0.003 | 21 |
| Drug Use Index | +0.34 | 0.009 | 22 |
| Outcome | Coefficient | p-value | N |
|---|---|---|---|
| Obesity | +2.69 | 0.020 | 21 |
| Maths/Literacy | -8.09 | 0.042 | 21 |
| Life Expectancy | -0.31 | 0.084 | 23 |
| Infant Mortality | +0.26 | 0.263 | 23 |
| Homicides | +1.84 | 0.385 | 23 |
\[H_0: \beta_1 = 0 \quad \text{(no relationship)}\]
If inequality truly had no effect, how likely would we observe coefficients this large?
Under \(H_0\), with probability \(p\) an outcome this extreme would occur.
But statistical significance is not causal evidence
\[\text{var}(\hat{\beta}) = \frac{\sigma^2}{n}\cdot\frac{1}{\text{var}(x_{i})}\]
Pre-existing indices provide credibility against cherry-picking
Some relationships may be driven by extreme observations:
| Outcome | Robust? |
|---|---|
| Trust | Yes |
| Mental Illness | Sensitive |
| Imprisonment | Sensitive to USA |
| Obesity | Yes |
Always check sensitivity to outliers
Inequality and social problems share a common cause, but inequality does not cause social problems.
Control for confounders to isolate causal effect
Stress is part of the causal pathway
Different designs answer similar questions with different assumptions
Empirical exercise 5